WALLIS (Dr. JOHN), in biography, an eminent English mathematician, was the son of a clergyman, and born at Ashford, in Kent, November 23, 1616. After be. ing instructed, at different schools, in grammar learning, in Latin, Greek, and Hebrew, with the rudiments of logic, music, and the French language, he was placed in Emanuel College, Cambridge. About 1640, he entered into orders, and was chosen Fellow of Queen's College. He kept his fellowship till it was vacated by his marriage, but quitted his college to be chaplain to Sir Richard Harley : after a year spent in this situation, he spent two more as chaplain to Lady Vere. While he lived in this family he cultivated the art of deciphering, which proved very useful to him on several occasions: he met with rewards and prefermentfrom the government at home for deciphering let ters for them; and it is said, that the Elec tor of Brandenburg sent him a gold chain and medal, for explaining for him some letters written in ciphers.
Acadeniical studies being much inter rupted by the civil wars in both the Uni versities, many learned men from them re sorted to London, and formed assemblies there. Wallis belonged to one of these, the members of which met once a week, to discourse on philosophical matters ; and this society was the rise and begin ning of that which was afterwards incor porated by the name of the Royal Society, of which Wallis was one of the most early members.
The Savilian professor of geometry at Oxford being ejected by the parliamentary visitors, in 1649, Wallis was appointed to succeed him, and he opened his lectures there the same year. In 1653, he publi shed, in Latin, a Grammar of the English Tongue, for the use of foreigners; to which was added, a tract " De Loquela seu Sonorum formatione," &c. in which he considers philosophically the formation of all sounds used in articulate speech, and shows how the organs being put into certain positions, and the breath pushed out from the lungs, the person will thus be made to speak, whether he hear him self or not. Pursuing these reflections, he was led to think it possible, that a deaf yerson might be taught to speak, by be ing directed so to apply the organs of speech as the sound of each letter requir ed, which children learn by imitation and frequent attempts, rather than by art.
In 1657, be collected and published his mathematical works, -in two parts, en titled " Mathesis Universalis," in quarto ; and, in 1658, " Commercium Epistolicum de Questionibus quibusdam Mathematicis nuper habitum," in quarto ; which was a collection of letters written by many learned men, as Lord Brounker, Sir Ke nelm Digby, Fermat, Schooten, Wallis, atid others.
Upon the Restoration he met with great respect ; the King thinking favourably of him on account of some services he had done both to himself and his father, Charles I. He was, therefore, confirmed in his places, also admitted one of the King's chaplains in ordinary, and appoint ed one of the divines empowered to re vise the Book of Common Prayer. He was a very useful member of the Royal Society, and kept up a literary corres pondence with many learned men.
In 1670, he published his " Mechanics; sive de Motu," quarto. In 1676, he gave an edition of " Archimedis Syracusani Arenarius et Dimensio Circuli ; and, in 1682, he published from the manuscripts, " Claudii Ptolemazi Opus Harmonicum," in Greek, with a Latin version and notes ; to which he afterwards added, " Appeit dix de veterum Harmonica ad hodiernam comparata," &c.
In 1685, he published his " History and Practice of Algebra," in folio ; a work that is full of learned and useful matter. Be sides the works above mentioned, he published many others, particularly his " Arithmetic;of Infinites," a book of genius and good invention, and perhaps almost his only work that is so, for he was much more distinguished for his industry and judgment, than for his genius. Also a multitude of papers in the Philosophical Transactions, in almost every volume, from the first to the twenty-fifth volume.
In 1697, the curators of the University press at Oxford thought it for the honour of the University to collect the Doctor's mathematical works, which had been printed separately, some in Latin, some in English, and published them all together in the Latin tongue, in three volumes, fo lio, 1699._ Dr. Wallis died at Oxford the 28th of October, 1703, in the eighty-eighth year of his age, leaving behind him one son and two daughters. We are told, that he was of a vigorous constitution, and of a mind which was strong, calm, serene, and not easily ruffled or discomposed. He speaks of himself, in his letter to Mr. Smith, in a strain which shows him to have been a very cautions and prudent man, whatever his secret opinions and attachments might be. He concludes; "It hath been my en, deavour all along, to act by moderate principles, being willing, whatever side was uppermost, to promote any good de-. sign, for the true interest of religion, of learning, and of the public good."